Eudoxos Hippopede Machine
the planets - retrograde motion - Aristotelian universe
What it shows:
This is the realization of a proposed solution to retrograde motion put
forward by Eudoxus (427 - 347 B.C.). Here a combination of three uniform
circular motions produces retrograde motion.
How it works:
The hippopede machine consists of three concentric rings, with a point on the
innermost representing the position of the planet. The assembly in figure
1 is held vertically in a 1.20m square Dexion™ metal frame. The outer
ring is made of 3cm wide 3mm steel; the inner rings of 3cm wide 1mm aluminum.
The outer ring is driven about its vertical axis by a 12V AC motor. The outer
ring rotates freely about its upper spindle that has gear wheel A (figure
2) stationary and gear wheel B turning with the outer ring. Gear wheel B is
linked through two right angle drives and two universal joints (with the connecting
rod supported by bearing guides attached to the outer ring) to the middle ring
which is driven about its horizontal axis. The inner ring is free to swing as
the middle ring turns. It is weighted to remain horizontal by a semicircular bow
of aluminum of equal radius to itself. As the apparatus moves, the spot on the
inner ring describes a circular horizontal orbit with two retrograde steps every
revolution.
table 1. Hippopede parameters
| Ring | Diameter (cm) | Rotation Speed (rpm) |
| Outer | 95 | 6.5 |
| Middle | 78 | 20 |
| Inner | 62 | 7 |
figure 1. The three circles of the Eudoxus Hippopede Machine
Comments:
Hippopede means horse-foot or horse-path. Horse training paths were typically laid
out in a figure 8, which is the kind of retrograde motion suggested by this model.
This machine, constructed by Bruce Collier, is designed to demonstrate the retrograde
loops of the planet Mercury. Its only fault is that the inner ring tends to oscillate
whereas it should always rotate in a fixed plane. Eudoxus, Plato's pupil, figured
that you only needed 26 simultaneous uniform motions to account for the motions of
all seven celestial bodies. Rating ***
figure 2. Detail of the outer to middle circle gearing system
